Math Problem Statement
Find an angle θ with 0° < θ < 360° that has the same sine and cosine values as 10°.
Solution
This question requires you to determine angles that share the same sine and cosine values as a given reference angle of , within the interval . Let me break it down for you:
Key Concepts:
-
Sine Symmetry: The sine of an angle is the same for and . It repeats every .
- For , the equivalent angle in the interval is:
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Cosine Symmetry: The cosine of an angle is the same for and . It also repeats every .
- For , the equivalent angle in the interval is:
Final Answers:
- Sine equivalent:
- Cosine equivalent:
Would you like more details or further assistance? Here are some related questions you could explore:
- What are the other symmetrical properties of trigonometric functions on the unit circle?
- How do sine and cosine relate to the unit circle visually?
- What happens if the angle is negative or exceeds ?
- How does symmetry in sine and cosine aid in solving equations?
- How would these results differ if the angle were given in radians?
Tip: Memorizing key unit circle angles and their symmetries will make these calculations much faster!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Unit Circle
Symmetry of Sine and Cosine
Formulas
sin(θ) = sin(180° - θ)
cos(θ) = cos(360° - θ)
Theorems
Symmetry Properties of Sine and Cosine
Suitable Grade Level
Grades 10-12